1. Introduction to
Statistical Quality Control

2. The contents of SQC
• Meaning statistical process control
• Control charts for variables
– R chart, ⎯X chart
• Control charts for attributes
– P chart, nP chart and c chart
• Acceptance sampling
– Producer’s & consumer’s risk

3. Statistical
Quality Control (SQC)
• Uses mathematics (i.e., statistics)
• Involves collecting data, organizing &
interpreting those collected data
• Objective: To Regulate product quality
• These are Used to
– Control the process as and when the
products are produced, and
– Inspect samples of finished products

4. Types of Statistical
Quality Control

5. • Characteristics for
which one focuses on
defects
• Classify products as
either ‘good’ or ‘bad’,
or count # defects
– e.g., radio works or not
• Categorical or discrete
random variables
Attributes
Attributes
Quality Characteristics
• Characteristics that
one can measure
– e.g., weight, length
• May be whole
number or fractional
• Continuous random
variables
Variables
Variables

6. Statistical
Process Control

7. Statistical
Process Control (SPC)
• Statistical technique used to ensure that
the process is making product to standard
• All process are subject to variability
– Natural causes: Random or chance
variations
– Assignable causes: Correctable problems
• Machine wear, unskilled workers, poor mat’l
• Objective: Identify assignable causes
• Uses process control charts

8. Purpose of Control Chart
• Show changes in data pattern
– e.g., trends
• Make corrections before process is out of
control
• Show causes of changes in data
– Assignable causes
• Data outside control limits or trend in data
– Natural causes
• Random variations around average

9. Statistical Process Control
Steps

10. Types of Control Chart
R X P C
R X P C
Continuous
Continuous
Numerical Data
Numerical Data
Categorical or
Categorical or
Discrete Numerical
Discrete Numerical
Data
Data

11. R Chart

12. R Chart
• Type of variables control chart
– Interval or ratio scaled numerical data
• Shows sample ranges over time
– Difference between smallest & largest
values in inspection sample
• Monitors variability in process
• Example: Weigh samples of coffee &
compute ranges of samples; Plot

13. R &⎯X Chart
Hotel Data
R &⎯X Chart
Hotel Data
Sample
Day Delivery Time Mean Range
1 7.30 4.20 6.10 3.45 5.55 5.32 3.85
7.30
7.30 -
- 3.45
3.45
Sample Range =
Sample Range =
Largest
Largest Smallest
Smallest

14. R &⎯X Chart
Hotel Data
Sample
Day Delivery Time Mean Range
1 7.30 4.20 6.10 3.45 5.55 5.32 3.85
2 4.60 8.70 7.60 4.43 7.62 6.59 4.27
3 5.98 2.92 6.20 4.20 5.10 4.88 3.28
4 7.20 5.10 5.19 6.80 4.21 5.70 2.99
5 4.00 4.50 5.50 1.89 4.46 4.07 3.61
6 10.10 8.10 6.50 5.06 6.94 7.34 5.04
7 6.77 5.08 5.90 6.90 9.30 6.79 4.22

15. ⎯X Chart
• Type of variables control chart
– Interval or ratio scaled numerical data
• Shows sample means over time
• Monitors process average
• Example: measure dimensions of
samples of components & compute
means of samples; & Plot the graph.

16. R &⎯X Chart
Some Data
Sample
Day Delivery Time Mean Range
1 7.30 4.20 6.10 3.45 5.55 5.32 3.85
2 4.60 8.70 7.60 4.43 7.62 6.59 4.27
3 5.98 2.92 6.20 4.20 5.10 4.88 3.28
4 7.20 5.10 5.19 6.80 4.21 5.70 2.99
5 4.00 4.50 5.50 1.89 4.46 4.07 3.61
6 10.10 8.10 6.50 5.06 6.94 7.34 5.04
7 6.77 5.08 5.90 6.90 9.30 6.79 4.22

17. • Solution*
• Redesign the process
• Use TQM tools
– Cause & effect diagrams
– Process flow charts
– Pareto charts
If the process is out of control
Method
Method People
People
Material
Material Equipment
Equipment
Too
Long

18. Acceptance Sampling

19. Statistical
Quality Control

20. What Is
Acceptance Sampling?
• It is a “Form of quality testing” used for
incoming materials or finished goods
– e.g., purchased material & components
• Procedure
– Take one or more samples at random from
a lot (shipment) of items
– Inspect each of the items in the sample
– Decide whether to reject the whole lot
based on the inspection results

21. What Is an
Acceptance Plan?
• It is a “Set of procedure” for inspecting
incoming materials or finished goods
• It Identifies
– Type of sample
– Sample size (n)
– Criteria (c) used to reject or accept a lot
• Producer (supplier) & consumer (buyer)
must negotiate

22. • Select a single random sample of
size n = 40 bags of potatoes from
a shipment (lot) of 200 bags.
• Determine the sample mean
weight,⎯X, of the 40 bags.
• If⎯X ≥ 39.5 Kgs., accept the
shipment (lot) of 200 bags;
otherwise reject it & inspect all
bags.
Example Sampling Plan for
Variables
© 1995 Corel Corp.

23. Operating Characteristics Curve
• Shows how well a sampling plan
discriminates between good & bad lots
(shipments)
• Shows the relationship between the
probability of accepting a lot & its quality

24. Producer’s & Consumer’s
Risk
• Producer's risk (α)
– Probability of rejecting a good lot
– Probability of rejecting a lot when fraction
defective is AQL
• Consumer's risk (ß)
– Probability of accepting a bad lot
– Probability of accepting a lot when fraction
defective is LTPD